It is shown that anyR[G]-ideal (-submodule) ofR(G)is contained in anR[G]-ideal (-submodule) of the formR(G)whereLis a left ideal (leftR-subgroup) of the near-ringR.For a connectedR-moduleNanR[G]-module structure is denned onN(G)such that if the near-ringRis 1-primitive onRNthenN(GM)is a faithful monogenicR[G]-module. Furthermore it is shown that ifNis a connectedR-module then there is a monomorphism fromEndRNintoEndR[G]N[G](as monoids). Finally a relationship is given between theJ½- andJ0-radical of the near-ringR.